Thick pseudomorphic nitride epitaxial layers

1. A semiconductor heterostructure comprising: an aluminum nitride single-crystal substrate; and at least one strained layer epitaxially grown thereover, the layer comprising at least one of AlN, GaN, InN, or any binary or tertiary alloy combination thereof, wherein a thickness of the strained layer exceeds a predicted critical thickness associated therewith by at least a factor of 5, as calculated with the Matthews-Blakeslee theory, h c = b 8 ⁢ π ⁢ ⁢ f ⁢ ( 1 - v ⁢ ⁢ cos 2 ⁢ α ) ( 1 + v ) ⁢ cos ⁢ ⁢ λ ⁢ ( ln ⁡ ( h c b ) + 1 ) , where h c is the predicted critical thickness, b is the magnitude of the Burgers vector of a dislocation formed between the layer and the substrate, f is the lattice mismatch between the layer and the substrate, υ is the Poisson's ratio of the layer, λ is the angle between the slip direction of the layer and the direction in the plane of the layer perpendicular to the line of intersection of the slip plane of the layer and the interface between the layer and the substrate, and α is the angle between the dislocation and the Burgers vector of the dislocation.

2. The semiconductor heterostructure of claim 1 , wherein the thickness of the at least one strained layer exceeds the predicted critical thickness by at least a factor of 10.

3. The semiconductor heterostructure of claim 1 , wherein the at least one strained layer is substantially free of In.

4. The semiconductor heterostructure of claim 1 , wherein the at least one strained layer has a density of macroscopic defects less than approximately 1 mm −2 .

5. The semiconductor heterostructure of claim 1 , wherein a strain parallel to the at least one strained layer is greater than 80% of a difference between parallel lattice parameters of an unstrained alloy of the same composition as the at least one strained layer and a relaxed platform disposed beneath the at least one strained layer.

6. The semiconductor heterostructure of claim 5 , wherein the at least one strained layer comprises Al x Ga 1-x N, the thickness of the at least one strained layer is greater than approximately 200 nm, and x is less than approximately 0.65.

7. The semiconductor heterostructure of claim 1 , wherein the thickness of the at least one strained layer is greater than approximately 1 μm.

8. The semiconductor heterostructure of claim 1 , wherein the at least one strained layer has an average threading dislocation density less than approximately 10,000 cm −2 .

9. A method for forming a semiconductor heterostructure, the method comprising: providing an aluminum nitride single-crystal substrate; and epitaxially depositing over the substrate a strained layer comprising at east one of AlN, GaN, InN, or any binary or tertiary alloy combination thereof, wherein a thickness of the strained layer exceeds a predicted critical thickness associated therewith by at least a factor of 5, as calculated with the Matthews-Blakeslee theory, h c = b 8 ⁢ π ⁢ ⁢ f ⁢ ( 1 - v ⁢ ⁢ cos 2 ⁢ α ) ( 1 + v ) ⁢ cos ⁢ ⁢ λ ⁢ ( ln ⁡ ( h c b ) + 1 ) , where h c is the predicted critical thickness, b is the magnitude of the Burgers vector of a dislocation formed between the layer and the substrate, f is the lattice mismatch between the layer and the substrate, υ is the Poisson's ratio of the layer, λ is the angle between the slip direction of the layer and the direction in the plane of the layer perpendicular to the line of intersection of the slip plane of the layer and the interface between the layer and the substrate, and α is the angle between the dislocation and the Burgers vector of the dislocation.

10. The method of claim 9 , further comprising forming a buffer layer over the substrate prior to depositing the strained layer.

11. The method of claim 10 , further comprising forming a graded layer between the buffer layer and the strained layer.

12. The method of claim 9 , wherein the thickness of the strained layer exceeds the predicted critical thickness by at least a factor of 10.

13. The method of claim 9 , wherein the strained layer is substantially free of In.

14. The method of claim 9 , wherein the strained layer has a density of macroscopic defects less than approximately 1 mm −2 .

15. The method of claim 9 , wherein the strained layer comprises AlGaN, and epitaxially depositing the strained layer comprises introducing trimethylaluminum and trimethylgallium into a reactor.

16. The method of claim 15 , wherein an initial flow rate of the trimethylgallium during the deposition of the strained layer is lower than a final trimethylgallium flow rate.

17. The method of claim 9 , wherein the aluminum nitride single-crystal substrate has an RMS surface roughness less than approximately 0.5 nm for a 10 μm×10 μm area, a surface misorientation between approximately 0.3° and 4°, and a threading dislocation density less than approximately 10 4 cm −2 .

18. The method of claim 9 , wherein a threading dislocation density of the strained layer is approximately equal to a threading dislocation density of the aluminum nitride single crystal substrate.

19. A device selected from the group consisting of a field effect transistor, a light-emitting diode, and a laser diode, the device comprising at least a portion of a strained heterostructure including: an aluminum nitride single-crystal substrate; and at least one strained layer epitaxially grown thereover, the layer comprising at least one of AlN, GaN, InN, or any binary or tertiary alloy combination thereof, wherein a thickness of the strained layer exceeds a predicted critical thickness associated therewith by at least a factor of 10, as calculated with the Matthews-Blakeslee theory, h c = b 8 ⁢ π ⁢ ⁢ f ⁢ ( 1 - v ⁢ ⁢ cos 2 ⁢ α ) ( 1 + v ) ⁢ cos ⁢ ⁢ λ ⁢ ( ln ⁡ ( h c b ) + 1 ) , where h c is the predicted critical thickness, b is the magnitude of the Burgers vector of a dislocation formed between the layer and the substrate, λ is the lattice mismatch between the layer and the substrate, υ is the Poisson's ratio of the layer, λ is the angle between the slip direction of the layer and the direction in the plane of the layer perpendicular to the line of intersection of the slip plane of the layer and the interface between the layer and the substrate, and α is the angle between the dislocation and the Burgers vector of the dislocation.

20. The device of claim 19 , wherein the device is a light-emitting diode comprising at least one interdigitated contact.

21. A device selected from the group consisting of a field effect transistor, a light-emitting diode, and a laser diode, the device comprising at least a portion of a strained heterostructure including: an aluminum nitride single-crystal substrate; and a plurality of strained layers epitaxially grown thereover, each of the plurality of strained layers comprising at least one of AlN, GaN, InN, or any binary or tertiary alloy combination thereof, wherein a total thickness of the plurality of strained layers exceeds a predicted critical thickness associated therewith by at least a factor of 10, as calculated with the Matthews-Blakeslee theory, h c = b 8 ⁢ π ⁢ ⁢ f ⁢ ( 1 - v ⁢ ⁢ cos 2 ⁢ α ) ( 1 + v ) ⁢ cos ⁢ ⁢ λ ⁢ ( ln ⁡ ( h c b ) + 1 ) , where h c is the predicted critical thickness, b is the magnitude of the Burgers vector of a dislocation formed between the layers and the substrate, f is the lattice mismatch between the layers and the substrate, υ is the Poisson's ratio of the layers, λ is the angle between the slip direction of the layers and the direction in the plane of the layers perpendicular to the line of intersection of the slip plane of the layers and the interface between the layers and the substrate, and α is the angle between the dislocation and the Burgers vector of the dislocation.

22. The device of claim 21 , wherein a lattice parameter parallel to the surface of the aluminum nitride single-crystal substrate of each of the plurality of strained layers is different from a lattice parameter of the aluminum nitride single-crystal substrate by less than 0.2%.

23. The semiconductor heterostructure of claim 1 , further comprising a relaxed cap layer disposed over the at least one strained layer.

24. The method of claim 9 , further comprising forming over the strained layer a relaxed cap layer, the strained layer remaining strained after formation of the relaxed cap layer.

25. The method of claim 9 , further comprising heating the substrate to approximately 1100° C. prior to epitaxially depositing the strained layer.

26. The method of claim 9 , wherein the strained layer is epitaxially deposited at a temperature ranging from greater than approximately 1100° C. to approximately 1300° C.

27. The device of claim 19 , further comprising a relaxed cap layer disposed over the at least one strained layer.

28. The device of claim 21 , further comprising a relaxed cap layer disposed over the plurality of strained layers.